Lange's method defines the triaxial stress/strain field in the pulley components. As such, metal fatigue limits can be applied from published literature on particular metal properties.

Metal fatigue limits vary with material properties, construction methods such as weldments, machining, and native surfaces, and with variations in fatigue loads.

Material properties can be found in technical publications with references to life defining limits including tensile strength, yield strength, and endurance limits for cyclic loading in tension, compression and shear.

You must also determine what stress or strain theory to apply such as distortion energy, Tresca, maximum-strain-energy, maximum normal-stress, Von Mises, and so on. The stress limits will differ. The theories encompass yield, endurance and cyclic loading limits.

Construction methods have separate stress limiting criteria associated with types of stresses based on whether the location of interest is native metal, weldments (fillets, butts, and plug welds), machined surfaces and polished surfaces, and manufacturing tolerances. British and American Standards welding tests and corresponding types of weld capacity are documented in these standards.

Although these standards have references to types of surface conditions they are quite conservative in stress limits where special treatment is used such as ground and polished.

The engineer can use other techniques such as likelihood or probability measures in quantifying confidence limits on a manufactured part.

Lange has some restrictions in that the work was published in 1963, well before computers were commonplace. He did not carry out the necessary Fourier expansion to its proper limits, which introduce errors in shell and end disk stresses. Furthermore, Lange did not appropriately treat the stress field between end disk and shell connection, as it should be. A discussion on this point can be found in the Bulk Solids Handling (BSH) publication: "A New Pulley Stress Analysis Method... by Qiu and Sethi in Vol 13 No. 4 November 1993.

You can apply fatigue history and histogram methods of analysis, which is seldom done in our industry.

This does not directly answer your questions, but does highlight the added information and technique that is required to provide a reasonable answer. The field is quite complex and is outside the domain of this forum. Anyone offering a single answer to your question does not know the field unless they apply heaps of qualifications.

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Dear Gareth,

The modern approach to engineered class pulleys uses the Goodman type endurance envelope of cycling tensile and compressive stresses verses mean stress levels.

The pulley stress levels you speak of 55 mpa ( 8000 psi) at steady-state and 70 mpa(10150 psi) for momentary are as you said ancient. I have looked at most pulley stress program concepts back to 1953 in the USA, Europe, Australia, and South Africa. CDI internally has 4 different versions ranging from your stresses and the methods of determining those stresses up to full FEA. Momentary stress levels are used when their level multiplied by 0.80 exceed the steady-state level. We do not use a different metal stress criteria.

Historical USA shell and end disk analysis methods used Timeshenko 1929 and 1940 methods or Roark's 1943 version pgs 191 (pt. 10) and 210 for end disk including thin and thick plate alternatives with rigid and flex disk to shell connections. The stress levels varied for the end disk between 7000 psi (48 mpa) peak and 9000 psi (62 mpa) depending if the end disk was welded or machined respectively.

Shell stress limits are 4000 psi (27.5 mpa) due to the type of welding and use of reinforcing (forming) rings. Note, the end disk to shell fillet weld has inherent flaws in the transfer of the shear and bending stresses due to the nature of the weld. This lead to the practice of welding the inside disk to shell connection.

Weld limits can be doubled (more or less) with proper machining of the weld zone with removal of all weld roughened surfaces. I do not want to elaborate on fillets at end disk and shell, and shell butt weld and inner ring welds.

Modern pulley design do not use these limits or methods of calculation. There are many examples of failures. I have applied die penetrant to many pulleys and investigated many failures for which modern design standards would detect. How about a large well known mfg. who installed over 50 engineered class pulleys in a value range of $200,000/ea. where over 20 were failing but were changed out for non-failure reasons just in time. One did not make the cut and caused $$$ damage. Investigation showed the mfg to be negligent over a 10 year period. Until that moment, the mfg had a voice that drowned out all dialog.

We have a specification that have been adopted by many major mfgrs. and large contractors (F, B, D, P, R, ....). Some say the CDI docs are similar to ASME codes but tailored to conveyor pulleys.

We have written papers on pulley design criteria as you can find on our website.

I can quote PSTRESS to your email. It is the CDI code that was written about by Dr. Qiu in BSH. It has the same accuracy as FEA including tapered end disks. It is a full triaxial analysis method with fatigue analysis procedure for the shell, end disk, locking device(Rf, Bikon, et al), hub and shaft. I do not know if you need such a complex code. ■

Look on my web site. I believe you can see the fluid factor and the fallen stacker in the photo. ■

Boy!!

Larry - U certainly pack the details in.

Just diverting the topic a little

You mentioned dye pne NDT testing on pulleys

I have used UT on the end disc to look at the butt weld - end dics/shell. This is OK but is restricted by the angle of the machined face of the end disc for the weld prep. So we can not see the front part of the butt weld.

I am led to beleive - from past NDT on some failed pulleys - that the cracks initiate from the inside - esp. where there is no internal weld run. Hence, UT is OK for this - U can even UT from the end of the shell.

Can U pls elaborate on your dye pen NDT - why did U choose this method......had the cracks reached the outside of the end disc. Usually, the cracks grow to the outside of the shell (under any lagging etc).

Thanks

James ■

Dear James,

I much appreciate the compliment.

Dye penetrant inspection is a poor man's quick and dirty field investigation tool for hub to disk welds. This use to be the dominant point of failure in my travels about the US and Canada pre 1980's.

Mag particle is debatably one step up from the dye, but also cannot see internal flaws.

Other major points of failure are the shell with the stiffener/forming internal ring and the connection of the end disk to shell. The internal ring is a misunderstood device and is prone to failure due to its application method.

I do agree that UT is the better tool, especially for these areas. It is better to see the potential for failure before the pulley is put into use. Proper UT inspection of weldments at disk to hub and shell requires special fixtures and techniques at reading the echo. Often the operator gets a false negative because of the difficulty of reading the sonic beam and having the proper transducer angle.

I concur with your belief. Many failures of the end disk to shell emanates from the weld stress riser at the internal terminus where the weld penetration stops. The crack then propagates from this internal weld stress riser on a 45 degree shear angle until it reaches the outer shell near or outside the end disk face on the shell OD. I have cut and sectioned many pulleys to study this type of failure.

When you take a step back and ask the question of strain flow, I wonder how so many pulleys have survivied. This is a question for another day.

This type of failure gave rise to internal welding of the disk-shell joint and of machined T-type turbine end disk configurations to negate this failure potential.

X-ray is yet another type of inspection that is not favored due to the use of isotope radiation danger. This technique is the most accurate, quantitative, costly and hazardous. ■

To be utterly pedantic,

The disk to shell weld flaw can be illustrated.

Imagine a crossection of end disk to shell with the weld penetrating to half way through the end disk thickness.

Note, the weld internal tip is highly irregular in its penetration and is the point of plasma cooling and highest point of weld inclusions.

Draw a simple sketch of the solid metal configuration with a gap between the shell ID and disk OD. Note, the gap is very small and enhances the stress riser when applying shaft bending action between end disk and shell that cycles to maximums (+/-) with a mean stress more or less equal to the locking device compressive stress plus or minus the belt reaction load per each rotation of the pulley.

The imagined crossection clearly illustrates the path of failure when you try to place a positive bending stress on the joint. ■

Larry

Thanks for the comments...

At our plant, we have designated this year as the "year of the crack". Will not go into details!!! But we need to work on preventing more failures after (only) 8 years running. Wonder who will give 10 year warranties on their gear against fatigue failures??!!!

Designers must produce a good design based on sound principles, they also must understand the limitations of the manufacturing methods and also enable suitable NDT methods to be applied to monitor the health of the equipment in the years to come.

Pulley design seems a funny (interesting) area.

We have two respected supplier belt bucket elevators on our site. One tried to follow the conventional conveyor design but fell foul on the SR on the inside weldment - butt from one side. They tackled the issue by going to a thicker shell - we did not take this up, went for welded both sides design.

The other has used a thick hub with keyway and a very thin end disc and a fillet weld connection to the thick shell. They claim no failures to date - but we have detected cracking from the toe of the fillet weld into the shell.

We aslo have conventional belt conveyors with the "simple" hub, thin end disc and shell design - one pulley (head/TU) on one has failed at the hub/end disc connection and the other one (drive) at the tail looks like going for ages - what gives!!!!

The application of the pulley design methods has other areas of application eg ball mill ends. We have suffered from "smart" design (shrink) techniques will very high remedial costs and the OEM reverting back to fully welded connections.

The other area of critical application is winches drums/end discs. I have found (designed in) partial penetration butt welds on key winches and this worries the hell out of me after the other failures. I do not understand the thinking of the designer in this case.

We are either faced with doing NDT (assuming that we can do it with a high degree of confidence or replacing/carrying the part to be sure)

Finally, just where on your web site is the photo of the stacker and pulley??

Cheers

James ■

Dear Zane,

Dr. Qiu's work I referred to in an earlier posting. His work corrects a flaw or omission in Lange's thesis. Lange could not transmit the bending moment and strain around the disk to shell joint. Therefore, the stress prediction fell short in addition to the short commings in the Fourier expansion terms of both disk and shell.

Dr. Qiu was able to use a feature in FEA to calculate the strain and moment in an elegant manner he coined as a Modified Transfer Matrix Method. He wanted to write a technical book on the method which has many applications in the sciences.

Prior to this solution, we investigated the method published in the Applied Mechanics Journal (I believe 1963 - Catholic University of America (Washington DC) ). The author studied chimney smoke stacks that had the concept of a Taylors Expansion Series to preserve the bending and strain fields from the cylinder to the stack base. Dr. Jean-Luc Cornet developed this work to the level on convergence of the series for cylinders on reasonable length to diameter. Short L/D were not solvable.

If you want Lange's work with all its warts, I will see how easy it is to retrieve it from our archives. Let me know.

Schmoltzi wrote a next step after Lange where he discusses locking device, hub and disk to shell stresses and end disk to shell alternative connections. He has a fatal flaw in the locking device formulation which we noted to him. His comment was so what! This was given to Ringfeder. They developed a analysis around the flaw.

Now FEM/FEA is commonly used. It too has problems in handling the 300-500 K degrees of freedom to do a proper analysis of the complete assembly. The belt method is using 2-D superposition and symmetric loading of one quadrant of the pulley. ■

I will request my staff to survey the archieved documents tomorrow.

German or English?

Anything to trade? ■

I did try a quick pass and found it is not in our alphbetic filing.

I am in India and will return Nov. 15. It is in a binder with similar papers. I need to do a binder by binder search. I ask your patience.

Otherwise go to Prok. Precismeca, or other manufacturers. If you have $$$ stick, I am sure they will comply. ■